Foam sheets of high compressive strength are produced by extruding a mixture of a styrene polymer and from 5 to 16 % by weight of a blowing agent mixture containing a) from 3 to 70 % by weight of an alcohol or ketone having a boiling point of from 56 to 100.degree.C, b) from 5 to 50 % by weight of carbon dioxide and c) from 0 to 90 % by weight of a saturated C3- to C5hydrocarbon and/or of a hydrogen-containing chlorofluorocarbon or fluorinated hydrocarbon boiling at from -30.degree. to +30.degree.C.